Ions that possess only one electron are referred to as hydrogen-like

CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

Ions that possess only one electron are referred to as hydrogen-like. The ground-state binding energy of a hydrogen atom is

-13.6\,\text{eV}

, while precision measurements show that the ground-state binding energy of the helium ion He

^{+}

-54.4\,\text{eV}

. (These values are provided for reference.) (a) Describe the pattern you observe when comparing the ground-state energies of H and He

^{+}

. State a physical principle that could account for this pattern. (b) Using the pattern identified in part (a), estimate the total energy of an electron in the state

n = 3

of He

^{+}

. (c) Determine the wavelength of the photon emitted when the electron in He

^{+}

undergoes the transition

n = 3 \rightarrow n = 2

. Present your answer in nanometres. (d) Compare the wavelength calculated in part (c) with the corresponding wavelength for the hydrogen transition

n = 3 \rightarrow n = 2

. Explain how differences in nuclear charge influence the positions of spectral lines among hydrogen-like species.

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